Estimating communication quality

ABSTRACT

A method for estimating quality of communications between a transmitter and a receiver over a communications link operable to carry data in at least one of a plurality of different compressed forms, the method comprising: detecting an error rate of the communications as received; receiving at a quality estimation unit an indication of the detected error rate and an indication of the at least one of the plurality of compressed forms in use over the link; and the quality estimation unit estimating the quality of the communications by means of both the indication of the detected error rate and the indication of the at least one of the plurality of compressed forms.

[0001] This invention relates to estimating communication quality, forexample to improving estimation of error rates in received data. Theinvention is preferably suitable for use in a telecommunications systemsuch as a cellular radio telecommunications network.

[0002]FIG. 1 shows schematically the configuration of a typical cellularradio telecommunications network such as a GSM (Global System for MobileCommunications) system. The network comprises a number of basetransmission stations (BTSS) 1, 2, 3. Each base-station has a radiotransceiver capable of transmitting radio signals to and receiving radiosignals from the area of a cell 4, 5, 6 etc. next to the base-station.By means of these signals the base-station can communicate with a mobilestation (MS) terminal 7 in that cell, which itself includes a radiotransceiver. Each base station is connected via a base stationcontroller 8 to a mobile switching centre (MSC) (not shown), which islinked in turn via a gateway MSC 9 to the public telephone network 10and/or to other networks such as packet data networks. By means of thissystem a user of the MS 7 can establish a telephone call to a terminal11 in another network.

[0003] The signals between a BTS and an MS carry digital data. Analoguevoice data to be carried over the link is encoded into digital datausing a suitable speech codec. The encoded data is then allocated totime slots and transmitted in those time slots to the recipient unit. Intypical TDMA systems a group of consecutive time slots (e.g. 8 timeslots in the GSM system) make up a TDMA frame. For example, in the GSMsystem TDMA frame is made up of 8 consecutive time slots. Up to 8different users at full data rate can be allocated to a single TDMAframe, each user having its own time slot. A slot may alternatively beshared between two users at half data rate, in which case those usersare allocated the same timeslot but in alternate TDMA frames. A user'sspeech data is carried in the frames allocated to that user. If the useris a full data rate user then a speech frame of the user will occupy onetimeslot of eight consecutive TDMA frames: for example if a TDMA framelasts for 4,615 ms (as in GSM), one speech frame will taking 8×4,615 msto be fully sent. If the user is a half data rate user his speech framecontains half as much data as that of a full rate user, and occupies onetimeslot of four alternate TDMA frames. Thus in GSM the total time takento transmit a half rate speech frame is essentially the same as the timetaken to transmit a full rate speech frame. At the recipient unit thedata is decoded to regenerate the analogue voice data. FIG. 2illustrates schematically the receiver path in the mobile station. (Theconsiderations at the BTS are analogous). Incoming received data at 20is passed to a decoder 21. The decoded analogue voice signals are passedto an output unit 22.

[0004] In typical systems the quality or error rate of the link isestimated by measuring characteristics of the received signal. A biterror rate (BER) before channel decoding can be estimated for thereceived digital bitstream, as indicated schematically at 23. The biterror rate represents the ration of badly received bits to the totalnumber of received bits. In addition, using check bits that aretransmitted as part of the bitstream the decoder 21 can detect badlyreceived voice data frames. This allows a frame erasure rate (FER) to bedetermined, as indicated schematically at 24. The frame erasure raterepresents the percentage of received frames being dropped due to a highnumber of non-corrected bit errors in the frame. Other methods can beused to determine whether a received frame is to be considered as bad.For example, if the BER before channel decoding is high the frame couldautomatically be assumed to be bad, even if the CRC would indicate thatthe frame was acceptable. This is especially significant in normal fullrate data reception, where the CRC occupies three bits, so even if plainnoise were sent one in eight frames could on average be taken to be avalid frame

[0005] In a typical system such as GSM the BER before channel decodingis estimated and that estimate reported to a control unit which cancontrol the system so as to maintain adequate link quality, for exampleby instructing an increase or decrease in transmission power or ahandover of an MS to another BTS.

[0006] The estimated BER before channel decoding is a direct indicationof the level of errors over the link and has therefore been used inprior systems as an indication of the quality of the link on which tobase such control measures. In the conventional GSM system only onevoice codec, or only very few codecs, have been available. Therefore, inmany cases the relationship between BER before channel decoding andperceived link quality has been easily predictable, although problemsexist for example between frequency hopping and non-hopping channels.However, with the implementation of more recent developments that makeuse of variable compression ratios and alternative error correctiontechniques—such as AMR (adaptive multirate), GPRS (general packet radioservice) and EGPRS (extended GPRS) or+ECSD equivalents—the BER becomes aless accurate indicator of true link quality, because the true qualityof received voice data as perceived by a user is also dependant on thelevel of compression and/or error correction that can be performed underthe protocols in use over the link. As the proportion of received bitsused for error correction increases relative to those used for encodedvoice data the potential for efficient error correction increases andBER before channel decoding becomes less accurate as an indicator oflink quality.

[0007] In the GSM system the conventional quality measure (RxQual) isbased on the pseudo bit-error rate (pseudoBER) or an estimate of the BERmade before channel decoding, which is an estimate of the bit errorsover the air interface. The (pseudo) BER is calculated before channeldecoding. While the robustness against channel errors in AMR operationsdepends on the codec mode in use, the real performance of the connectioncannot be estimated from RxQual alone: knowledge of the codec mode inuse is needed. Moreover, since the theoretical maximum link adaptationrate of AMR is 1140 ms, the codec mode can change several (up to amaximum of 12) times during the normal measurement period of GSM (480ms). This means that the actual BER (after channel decoding) (and FER)of the connection depends on the raw bit error rate of each trafficchannel (TCH) frame during the connection and the codec modes used inthose frames.

[0008] The correct quality information is especially important forhandover and power control algorithms where one of the most importantcriterion to increase or decrease the transmit powers or trigger thehandovers is the quality of the connection.

[0009]FIG. 3 illustrates AMR codec modes. An example of simulationresults where the most robust codec mode of AMR was used is shown inFIG. 4. Note that while the connection quality was in lowest RXQUALclass for several seconds during the simulation, the amount of actualframe erasures was still acceptable. In normal FR connection this wouldhave meant a significant break in the speech or even a dropped call.

[0010] One option to provide a more accurate measure of quality would beto send measured uplink FER information from BTS to BSC. However, thiswould only address the quality measurement problems of the uplinkbecause downlink FER is not available in current GSM systems. This isespecially significant since the downlink is normally considered to bethe limiting path in terms of interference. Another option would be touse the normal RXQUAL measure in handover and power control and to setthe RXQUAL thresholds according, for example, to the performance ofsignaling channels. This would however mean a compromise in theperformance tuning of AMR especially if only high modes of the AMR wereused.

[0011] There is therefore a need for a means of providing a moreaccurate indicator of link quality, for example to allow link quality tobe better controlled.

[0012] According to one aspect of the present invention there isprovided a method for estimating quality of communications between atransmitter and a receiver over a communications link operable to carrydata in at least one of a plurality of different compressed forms, themethod comprising: detecting an error rate of the communications asreceived; receiving at a quality estimation unit an indication of thedetected error rate and an indication of the at least one of theplurality of compressed forms in use over the link; and the qualityestimation unit estimating the quality of the communications by means ofboth the indication of the detected error rate and the indication of theat least one of the plurality of compressed forms.

[0013] According to a second aspect of the present invention there isprovided a communications system comprising: a transmitter and areceiver capable of communicating over a communications link operable tocarry data in at least one of a plurality of different compressed forms;error rate detection apparatus for detecting an error rate of thecommunications as received; and a quality estimation unit for receivingan indication of the detected error rate and an indication of the atleast one of the plurality of compressed forms in use over the link, andestimating the quality of the communications by means of both theindication of the detected error rate and the indication of the at leastone of the plurality of compressed forms.

[0014] According to a third aspect of the present invention there isprovided a network element for operation in a communications system inwhich a transmitter and a receiver can communicate over a communicationslink operable to carry data in at least one of a plurality of differentcompressed forms; the network element comprising: a transmitter or areceiver capable of communicating over a communications link operable tocarry data in at least one of a plurality of different compressed forms;error rate detection apparatus for detecting an error rate of thecommunications as received; and a quality estimation unit for receivingan indication of the detected error rate and an indication of the atleast one of the plurality of compressed forms in use over the link, andestimating the quality of the communications by means of both theindication of the detected error rate and the indication of the at leastone of the plurality of compressed forms.

[0015] The data is preferably speech data, but could be other data suchas video data or text data. The data is suitably carried in digitalform.

[0016] The different compressed forms are suitably forms resulting fromcompression by different codecs. Those codecs may together form amulti-rate coding scheme. The multi-rate coding scheme may involve theselection from time to time of one of the codecs from the set on thebasis of detected conditions of the link.

[0017] The error rate may be an estimation of bit error rate, preferablybefore channel decoding, or a pseudo bit error rate. Other measures oferror rate may be used, especially in systems other than the GSM system.

[0018] One of the transmitter and the receiver may be a basetransmission station. The base transmission station may be under thecontrol of a base station controller. The other of the transmitter andreceiver is a mobile station. The receiver unit may also be capable oftransmitting signals to the transmitter, which may be capable ofreceiving them.

[0019] The quality estimation unit may be located at the base stationcontroller.

[0020] The link may be a traffic channel. The link may be part of aradio communications channel between the transmitter and the receiver,which may also include control channels.

[0021] The indication of the detected error rate suitably includesinformation indicative of a detected error rate for communications overthe link from the transmitter to the receiver (and suitably from thereceiver to the transmitter). Data over the link is sent in the form ofdata frames and the indication of the detected error rate includes avalue of error rate for each frame for communications from thetransmitter to the receiver, and an average value of error rate for aplurality of frames for communications from the receiver to thetransmitter. In this case, preferably the receiver is a mobile stationand the transmitter is a base transmission station.

[0022] Suitably the indication of the detected error rate includes anaverage value of error rate for a plurality of frames for communicationsfrom the transmitter to the receiver.

[0023] Suitably data over the link is sent from the transmitter to thereceiver in the form of data frames and the indication of at least oneof the plurality of compressed forms comprises an indication of one ofthe forms for each of the frames.

[0024] Data over the link may be sent from the transmitter to thereceiver in the form of data frames and the indication of at least oneof the plurality of compressed forms comprises an indication of one ofthe forms for only some of the frames. The data over the link is sentfrom the transmitter to the receiver in the form of groups of dataframes and the indication of at least one of the plurality of compressedforms comprises an indication of one of the forms for the first frame ofeach group and an indication of one of the forms for the last frame ofeach group. The groups may be multiframes. The frames may be sent in oneor more TDMA frames. Each TDMA frame preferably occupies 4.615 ms. Forexample, in the GSM system TDMA frame is made up of 8 consecutive timeslots. Up to 8 different users at full data rate can be allocated to asingle TDMA frame, each user having its own time slot. A slot mayalternatively be shared between two users at half data rate, in whichcase those users are allocated the same timeslot but in alternateframes. A user's speech data is carried in the frames allocated to thatuser. If the user is a full data rate user then a speech frame of theuser will occupy one timeslot of eight consecutive TDMA frames: forexample if a TDMA frame lasts for 4,615 ms (as in GSM), one speech framewill taking 8×4,615 ms to be fully sent. If the user is a half data rateuser his speech frame contains half as much data as that of a full rateuser, and occupies one timeslot of four alternate TDMA frames. Thus inGSM the total time taken to transmit a half rate speech frame isessentially the same as the time taken to transmit a full rate speechframe. Each group of frames preferably comprises 24 frames, or 26 framesincluding traffic and control frames. The data over the link is suitablysent from the transmitter to the receiver in the form of groups of dataframes and the indication of at least one of the plurality of compressedforms comprises an indication of one of the forms for a single frame ofeach group. The groups may be multiframes. Each group of framespreferably comprises 24 frames, or 26 frames including traffic andcontrol frames.

[0025] Each group of frames suitably corresponds to a measurementperiod. The said averaging of error rates is preferably performed overthat period, or over a longer period.

[0026] The method may comprise the step of limiting the transmitter andthe receiver to using a single one of the compressed forms over the linkin each measurement period, which may be a multiframe.

[0027] The transmitter and the receiver are preferably operableaccording to the Global System for Mobile Communications or a derivativethereof.

[0028] The present invention will now be described by way of examplewith reference to the accompanying drawings, in which

[0029]FIG. 1 shows schematically a cellular network;

[0030]FIG. 2 illustrates data reception;

[0031]FIG. 3 illustrates AMR codec modes;

[0032]FIG. 4 shows simulated results of a the correlation between BFIand RxQual value (for FIXED codec mode: 4.75 kbit/s, dynamic channelprofile “es11”, full-rate channel, GSM downlink); and

[0033]FIG. 5 is a schematic diagram of relevant parts of a GSM cellularnetwork.

[0034] The present example will be described with specific reference tothe GSM system. However, the invention is not limited to application inthe GSM system.

[0035] This invention is particularly advantageous in conjunction withthe GSM Adaptive Multi-Rate (AMR) feature. AMR is an ETSI (EuropeanTelecommunications Standards Institute) specified next generation speechcodes for GSM networks. The AMR codec consists of a family of codecs(source and channel codecs with different trade-off bit-rates) operatingin the GSM full-rate (FR) and half-rate (HR) channels.

[0036] The ETSI AMR codec concept is intended to be capable of adaptingits operation optimally according to the prevailing radio channelconditions. At the AMR receiving end (of the radio channel), the qualityof the transmission is measured. Since the control of the used codecmode (source coding vs. channel coding bit-rate) is performed by theBTS, the mobile station is only able to send requests of appropriatedownlink (DL) codec mode, which may be overwritten by the system. Theserequests are sent in-band in the uplink (UL) channel. The control of theUL codec mode by the BTS is based on quality measurements performed bythe mobile station and/or the BTS itself. Using this information the BTSforces the mobile to use an appropriate codec mode by means of a codecmode command sent in-band on the downlink to mobile station. Inhigh-error conditions more bits are used for error correction to obtainerror robust coding, while in good transmission conditions only arelatively low proportion of bits is needed for sufficient errorprotection and more bits can therefore be allocated for source coding.

[0037] In the present approach, in order to be able to derive a morerepresentative estimate of real connection quality onto which the RXQUALsettings may be mapped, an indication of the codec mode(s) in use on theuplink and/or the downlink is sent to the BSC. Using that informationthe BSC can perform handover and power control calculations, mapping theRXQUAL into a more realistic quality estimate, which may represent aframe erasure probability (FEP).

[0038] In the GSM system each multiframe provides 26 frames, of which agroup of 24 frames are allocated for carrying traffic speech data forone user, and may therefore carry data encoded according to a selectedspeech codec. Signaling capacity limitations on the Abis interface(between the BTS and the BSC) mean that there are several possibilitiesfor conveniently sending the necessary information to the BSC.

[0039] 1) In a first route, the BSC would be sent informationindicating:

[0040] a) the codec used for each one of the 24 traffic channel frameson the uplink;

[0041] b) the codec used for each one of the 24 traffic channel frameson the downlink;

[0042] c) a RXQUAL (BER before channel decoding) value for each of the24 traffic channel frames on the uplink;

[0043] d) an average RXQUAL value for a plurality of frames of thedownlink—preferably the 24 traffic frames of a single multiframe; (theRXQUAL of each individual DL frame is not available).

[0044] 2) In a second route, the BSC would be sent for the uplink or thedownlink or both, information indicating:

[0045] a) the codec used in the first and last of the traffic channelframes of a multiframe;

[0046] b) RXQUAL information averaged over a measurement period (whichcould suitably be the period of a multiframe).

[0047] 3) In a third route, for the uplink or the downlink or both, theAMR scheme could be restricted so that link adaptation occurs only every{fraction (1/480)} ms, between multiframes. This would have the effectthat the codec in use would remain constant throughout a multiframe.Then, for the uplink or the downlink or both, the BSC would be sentinformation indicating:

[0048] a) the codec mode in use during the multiframe; and

[0049] b) RXQUAL information averaged over a measurement period (whichcould suitably be the period of a multiframe).

[0050] Naturally also other alternatives are possible

[0051] The performance of the above mentioned routes is compared below.

[0052] The first route offers the best accuracy combined with the mostflexible link adaptation (there being no restrictions on link adaptationrate). The third route is able to give the same accuracy in qualityassessment, but the ability to react fast to changes in the channel isworse since the operation of the AMR system is restricted. Simulationsperformed by the applicant have indicated that this factor is generallynot critical to performance: route 3 was able to offer even better linkperformance in certain simulations, especially in half rate mode. Thereason for this is believed to be that in some cases the link wasadapted even too aggressively in fast link adaptation while the actuallink quality had already changed to opposite direction. Secondly, thefirst route consumes a significant amount of Abis signaling capacity,which may easily cause problems if the additional TRX-signaling is nottaken into account in network planning. The second route offers acompromise in terms of quality estimation accuracy, as the actualquality has to be estimated as an average over used codec modes togetherwith the RXQUAL information.

[0053] When the BSC has the knowledge of used codes modes and the RXQUALassociated to those modes, it can use a simple mapping table to convertthe RXQUAL values into real connection quality or FEP, which can be usedfor example as a trigger in handover and power control algorithms.

[0054]FIG. 5 illustrates the architecture of a GSM system forimplementing a preferred embodiment of the invention. FIG. 5 shows amobile station 40 in radio communication with a base transmissionstation 41 over a wireless link 42. The antennae 43, 44 of the mobilestation and the BTS are connected to respective duplexers 45, 46 whichcombine the incoming and outgoing signals. The generation of theoutgoing signals for transmission is not illustrated in FIG. 5. Theincoming signals are passed to respective amplification and demodulationunits 47, 48 which derive received digital bitstreams at 49, 50. In themobile station the received bitstream is processed by decoding apparatusshown generally at 51 to decode the data and derive an analogue speechsignal at 52. The speech signal is applied to a loudspeaker 53 so thatit can be heard by a user. In the BTS the received digital signal at 50is transformed into a signal suitable for onward transmission to BSC 54by means of processing unit 55.

[0055] The transmission power used over the link 42, the codec used forspeech transmission over link 42, the estimated RXQUAL for link 42 andother parameters such as handover operations are under the control of aunit such as BSC 54. These parameters are transmitted from that controlunit via link 56 to the respective MS and BTS units to allow them toencode, transmit and decode their signals accordingly.

[0056] In the units 51 and 55 are respective error rate detectors 57, 58which determine error rates (suitably BER before channel decoding(including pseudo bit-error rates) or frame erasure rates) for receivedsignals. (It should be noted that at least the mobile station does nothave to calculate any statistical value of the frame errors (e.g. rate);instead the mobile could check the speech frames—frame by frame—and if aframe were found to have too many errors it could be not directed to theaudio equipment of the mobile station. In that case the unit 51 could beomitted.) The error rate data is reported, together with data indicatingthe codec(s) in use (for example, as in one of the reporting routesdiscussed above) to the control unit—in this example BSC 54. The BSC 54includes a handover/power-control processing unit 59 which uses thatdata to determine whether a modification of the communicationsoperations between the BTS and the MS is needed. Such a modification maytake the form of an increase or decrease in target RXQUAL (which mayresult in an increase or decrease in transmission power over the linkbetween the BTS and the MS) or hard and/or soft handover commands tocause the MS to communicate with another base station.

[0057] By making use of knowledge of both the error rate and the datacompression and/or encoding scheme in use over the link the BSC can makebetter decisions on the adjustment of RXQUAL targets, reducing the riskof RXQUAL being increased when high bit-error rates are being at leastpartly compensated for by compression schemes with high levels ofredundancy, or being reduced when even low bit-error rates are beinginadequately compensated for by compression schemes with low levels ofredundancy.

[0058] Numerous modifications of the specific examples described abovemay be made. For example, the calculations may be performed by anotherunit than the BSC—for example an MSC. The approaches described above maybe applied individually to the uplink or to the downlink, or to both.The approaches described above may be implemented in telecommunicationssystems operable according to other systems and standards, for examplethe third generation (3G) standard. In a system operable according tothat standard the MSC, rather than the BSC, could handle handover andpower control analysis. Reporting of data to the MSC could be performedover the lu interface.

[0059] The applicant draws attention to the fact that the presentinvention may include any feature or combination of features disclosedherein either implicitly or explicitly or any generalisation thereof,without limitation to the scope of any of the present claims. In view ofthe foregoing description it will be evident to a person skilled in theart that various modifications may be made within the scope of theinvention.

1. A method for estimating quality of communications between atransmitter and a receiver over a communications link operable to carrydata in at least one of a plurality of different compressed forms, themethod comprising: detecting an error rate of the communications asreceived; receiving at a quality estimation unit an indication of thedetected error rate and an indication of the at least one of theplurality of compressed forms in use over the link; and the qualityestimation unit estimating the quality of the communications by means ofboth the indication of the detected error rate and the indication of theat least one of the plurality of compressed forms.
 2. A method asclaimed in claim 1, wherein the data is speech data.
 3. A method asclaimed in any preceding claim, wherein the different compressed formsare forms resulting from compression by different codecs.
 4. A method asclamed in claim 3, wherein the codecs together form a multi-rate codingscheme.
 5. A method as claimed in claim 4, wherein the speech encodingscheme is an adaptive multi-rate encoding scheme.
 6. A method as claimedin any preceding claim, wherein the error rate is a bit error rate or apseudo bit error rate.
 7. A method as claimed in any preceding claim,wherein one of the transmitter and the receiver is a base transmissionstation under the control of a base station controller and the other ofthe transmitter and receiver is a mobile station.
 8. A method as claimedin claim 7, wherein the quality estimation unit is located at the basestation controller.
 9. A method as claimed in any preceding claim,wherein the link is a traffic channel.
 10. A method as claimed in anypreceding claim, wherein the indication of the detected error rateincludes information indicative of a detected error rate forcommunications over the link from the transmitter to the receiver andfrom the receiver to the transmitter.
 11. A method as claimed in claim10, wherein data over the link is sent in the form of data frames andthe indication of the detected error rate includes a value of error ratefor each frame for communications from the transmitter to the receiver,and an average value of error rate for a plurality of frames forcommunications from the receiver to the transmitter.
 12. A method asclaimed in claim 11, wherein the receiver is a mobile station and thetransmitter is a base transmission station.
 13. A method as claimed inany of claims 1 to 9, wherein the indication of the detected error rateincludes an average value of error rate for a plurality of frames forcommunications from the transmitter to the receiver.
 14. A method asclaimed in any preceding claim, wherein data over the link is sent fromthe transmitter to the receiver in the form of data frames and theindication of at least one of the plurality of compressed formscomprises an indication of one of the forms-for each of the frames. 15.A method as claimed in any of claims 1 to 13, wherein data over the linkis sent from the transmitter to the receiver in the form of data framesand the indication of at least one of the plurality of compressed formscomprises an indication of one of the forms for only some of the frames.16. A method as claimed in claim 15, wherein the data over the link issent from the transmitter to the receiver in the form of groups of dataframes and the indication of at least one of the plurality of compressedforms comprises an indication of one of the forms for the first frame ofeach group and an indication of one of the forms for the last frame ofeach group.
 17. A method as claimed in claim 15, wherein the data overthe link is sent from the transmitter to the receiver in the form ofgroups of data frames and the indication of at least one of theplurality of compressed forms comprises an indication of one of theforms for a single frame of each group.
 18. A method as claimed in claim16 or 17, wherein each group of frames corresponds to a measurementperiod.
 19. A method as claimed in claim 18, wherein said measurementperiod is 480 ms.
 20. A method as claimed in any preceding claim,comprising the step of limiting the transmitter and the receiver tousing a single one of the compressed forms over the link in eachmeasurement period.
 21. A method as claimed in any preceding claim,wherein the transmitter and the receiver are operable according to theGlobal System for Mobile Communications or a derivative thereof
 22. Acommunications system comprising: a transmitter and a receiver capableof communicating over a communications link operable to carry data in atleast one of a plurality of different compressed forms; error ratedetection apparatus for detecting an error rate of the communications asreceived; and a quality estimation unit for receiving an indication ofthe detected error rate and an indication of the at least one of theplurality of compressed forms in use over the link, and estimating thequality of the communications by means of both the indication of thedetected error rate and the indication of the at least one of theplurality of compressed forms.
 23. A network element for operation in acommunications system in which a transmitter and a receiver cancommunicate over a communications link operable to carry data in atleast one of a plurality of different compressed forms; the networkelement comprising: a transmitter or a receiver capable of communicatingover a communications link operable to carry data in at least one of aplurality of different compressed forms; error rate detection apparatusfor detecting an error rate of the communications as received; and aquality estimation unit for receiving an indication of the detectederror rate and an indication of the at least one of the plurality ofcompressed forms in use over the link, and estimating the quality of thecommunications by means of both the indication of the detected errorrate and the indication of the at least one of the plurality ofcompressed forms.